OK what you are looking for is a red and black checkered box/texture. These can be found in the skies textures or the one I use is in the bespin textures. Click one off them i.e skyplatform (bespin) and make a box with it around the map. Then hollow the box and this should make the sky and the left, right and bottom of the sky. The hollow button is found on the tool bar under file, view etc... Then once you have done this save and compile your map..

Im sure someone could explian it more clearly, but I have tried hope that helps...

When you select sky textures in Radiant, you'll get lots of textures in you texture window. Some on them look like skies and sceneries already, but unfortunately, those are not the ones you are going to use. Instead, you must select one of those tiny, black and white squares (shaders) that give no information about the actual scenery, except their name. Although you may guess something based on the textures with similar names. Then paint all (visible) sides on your skybox with that same shader, no need to worry about directions.

Yet, it depends on the shader itself if it gives or not any light to your map. For some shaders has the ability in its settings where another may have been set dark, nonluminous. In order to find out those settings, you must try, or use ShaderED.